An adaptive fast multipole accelerated Poisson solver for complex geometries

T. Askham, A. J. Cerfon

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


We present a fast, direct and adaptive Poisson solver for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the solver relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition. The volume integral is computed by applying the FMM on a square box that encloses the domain of interest. For the sake of efficiency and convergence acceleration, we first extend the source distribution (the right-hand side in the Poisson equation) to the enclosing box as a C0 function using a fast, boundary integral-based method. We demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and, as a result, to an extremely efficient “black box” fast solver.

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalJournal of Computational Physics
StatePublished - Sep 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Fast multipole method
  • Integral equations
  • Poisson equation
  • Quadrature by expansion


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